# Full text of "Analytical Mechanics"

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```246                      ANALYTICAL MECHANICS
198. Coefficient of Restitution. — It is found by experiment that the ratio of the impulse of restitution to the impulse of compression depends only upon the nature of the bodies in collision. The ratio, therefore, is a constant of the substances in collision. This constant is called the coefficient of restitution, and is generally denoted by the letter e. Thus
6=-|-                                      (IX)
Vi — v
Eliminating v we obtain
But (vi — tfc) and ( — Vi + v%} are the velocities of the first body relative to the second, just before and just after the collision. Denoting them by V and V, respectively, we obtain
vf e=£                               .             (X)
velocity after impact
relative velocity before impact
199. Resiliency. — When two bodies rebound after collision they are said to have resiliency, and the contact is called elastic contact. The coefficient of restitution is a measure of the resiliency of the colliding bodies. When e= 1 the resiliency of the colliding bodies is perfect and the contact is said to be perfectly elastic.
The coefficient of restitution cannot have a value greater than unity, as will be seen from a consideration of the transformation of energy which takes place during collision. At the beginning of the collision the bodies have a certain amount of kinetic energy which depends upon their relative```